LMFDB - Embedded newform 2100.2.ce.c.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(157,2100)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2100.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.ce (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.3
Character	$\chi$	$=$	2100.157
Dual form			2100.2.ce.c.1993.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{3} +(-1.18454 - 2.36577i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{3} +(-1.18454 - 2.36577i) q^{7} +(0.866025 - 0.500000i) q^{9} +(-2.25649 + 3.90835i) q^{11} +(-4.37238 - 4.37238i) q^{13} +(1.16804 + 4.35920i) q^{17} +(2.51045 + 4.34823i) q^{19} +(1.75649 + 1.97857i) q^{21} +(5.40108 + 1.44721i) q^{23} +(-0.707107 + 0.707107i) q^{27} +(-3.92124 - 2.26393i) q^{31} +(1.16804 - 4.35920i) q^{33} +(0.448288 - 1.67303i) q^{37} +(5.35505 + 3.09174i) q^{39} -2.22509i q^{41} +(7.85281 - 7.85281i) q^{43} +(12.4411 + 3.33357i) q^{47} +(-4.19371 + 5.60471i) q^{49} +(-2.25649 - 3.90835i) q^{51} +(-3.17491 - 11.8489i) q^{53} +(-3.55031 - 3.55031i) q^{57} +(1.11255 - 1.92699i) q^{59} +(6.34248 - 3.66183i) q^{61} +(-2.20873 - 1.45654i) q^{63} +(4.84982 - 1.29950i) q^{67} -5.59161 q^{69} +14.3670 q^{71} +(-4.19308 + 1.12353i) q^{73} +(11.9192 + 0.708707i) q^{77} +(1.58312 - 0.914012i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-11.2105 - 11.2105i) q^{83} +(3.90835 + 6.76946i) q^{89} +(-5.16475 + 15.5233i) q^{91} +(4.37357 + 1.17190i) q^{93} +(-3.53553 + 3.53553i) q^{97} +4.51298i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 8 q^{11} - 4 q^{21} - 60 q^{31} - 8 q^{51} + 84 q^{61} + 112 q^{71} + 12 q^{81} - 136 q^{91}+O(q^{100}) $ 24 * q - 8 * q^11 - 4 * q^21 - 60 * q^31 - 8 * q^51 + 84 * q^61 + 112 * q^71 + 12 * q^81 - 136 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.18454	−	2.36577i	−0.447716	−	0.894176i
$7$	−1.18454	−	2.36577i	−0.447716	−	0.894176i
$8$		0			0
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	−2.25649	+	3.90835i	−0.680357	+	1.17841i	0.294515	+	0.955647i	$0.404842\pi$
$11$	−2.25649	+	3.90835i	−0.680357	+	1.17841i	−0.974872	+	0.222766i	$0.928492\pi$
$12$		0			0
$13$	−4.37238	−	4.37238i	−1.21268	−	1.21268i	−0.970142	−	0.242537i	$-0.922020\pi$
$13$	−4.37238	−	4.37238i	−1.21268	−	1.21268i	−0.242537	−	0.970142i	$-0.577980\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.16804	+	4.35920i	0.283292	+	1.05726i	0.950078	+	0.312012i	$0.101003\pi$
$17$	1.16804	+	4.35920i	0.283292	+	1.05726i	−0.666786	+	0.745249i	$0.732330\pi$
$18$		0			0
$19$	2.51045	+	4.34823i	0.575937	+	0.997552i	0.995939	+	0.0900286i	$0.0286958\pi$
$19$	2.51045	+	4.34823i	0.575937	+	0.997552i	−0.420003	+	0.907523i	$0.637971\pi$
$20$		0			0
$21$	1.75649	+	1.97857i	0.383297	+	0.431760i
$22$		0			0
$23$	5.40108	+	1.44721i	1.12620	+	0.301765i	0.773391	−	0.633929i	$-0.218559\pi$
$23$	5.40108	+	1.44721i	1.12620	+	0.301765i	0.352812	+	0.935694i	$0.385226\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	−3.92124	−	2.26393i	−0.704275	−	0.406613i	0.104663	−	0.994508i	$-0.466624\pi$
$31$	−3.92124	−	2.26393i	−0.704275	−	0.406613i	−0.808938	+	0.587894i	$0.799957\pi$
$32$		0			0
$33$	1.16804	−	4.35920i	0.203330	−	0.758839i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.448288	−	1.67303i	0.0736980	−	0.275045i	−0.919237	−	0.393705i	$-0.871193\pi$
$37$	0.448288	−	1.67303i	0.0736980	−	0.275045i	0.992935	+	0.118660i	$0.0378599\pi$
$38$		0			0
$39$	5.35505	+	3.09174i	0.857494	+	0.495074i
$40$		0			0
$41$		−	2.22509i		−	0.347501i	−0.984790	−	0.173751i	$-0.944411\pi$
$41$		−	2.22509i		−	0.347501i	0.984790	−	0.173751i	$-0.0555887\pi$
$42$		0			0
$43$	7.85281	−	7.85281i	1.19754	−	1.19754i	0.222642	−	0.974900i	$-0.428532\pi$
$43$	7.85281	−	7.85281i	1.19754	−	1.19754i	0.974900	−	0.222642i	$-0.0714682\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	12.4411	+	3.33357i	1.81471	+	0.486251i	0.996111	−	0.0881077i	$-0.0280820\pi$
$47$	12.4411	+	3.33357i	1.81471	+	0.486251i	0.818604	+	0.574359i	$0.194749\pi$
$48$		0			0
$49$	−4.19371	+	5.60471i	−0.599101	+	0.800673i
$50$		0			0
$51$	−2.25649	−	3.90835i	−0.315972	−	0.547279i
$52$		0			0
$53$	−3.17491	−	11.8489i	−0.436107	−	1.62757i	−0.738404	−	0.674359i	$-0.764420\pi$
$53$	−3.17491	−	11.8489i	−0.436107	−	1.62757i	0.302297	−	0.953214i	$-0.402247\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.55031	−	3.55031i	−0.470250	−	0.470250i
$58$		0			0
$59$	1.11255	−	1.92699i	0.144841	−	0.250873i	−0.784472	−	0.620164i	$-0.787066\pi$
$59$	1.11255	−	1.92699i	0.144841	−	0.250873i	0.929314	+	0.369291i	$0.120399\pi$
$60$		0			0
$61$	6.34248	−	3.66183i	0.812071	−	0.468849i	−0.0356037	−	0.999366i	$-0.511335\pi$
$61$	6.34248	−	3.66183i	0.812071	−	0.468849i	0.847674	+	0.530517i	$0.178002\pi$
$62$		0			0
$63$	−2.20873	−	1.45654i	−0.278274	−	0.183507i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.84982	−	1.29950i	0.592499	−	0.158760i	0.0499041	−	0.998754i	$-0.484108\pi$
$67$	4.84982	−	1.29950i	0.592499	−	0.158760i	0.542595	+	0.839994i	$0.317442\pi$
$68$		0			0
$69$	−5.59161			−0.673151
$70$		0			0
$71$	14.3670			1.70504			0.852522	−	0.522692i	$-0.175072\pi$
$71$	14.3670			1.70504			0.852522	+	0.522692i	$0.175072\pi$
$72$		0			0
$73$	−4.19308	+	1.12353i	−0.490763	+	0.131500i	−0.495710	−	0.868488i	$-0.665092\pi$
$73$	−4.19308	+	1.12353i	−0.490763	+	0.131500i	0.00494658	+	0.999988i	$0.498425\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	11.9192	+	0.708707i	1.35831	+	0.0807646i
$78$		0			0
$79$	1.58312	−	0.914012i	0.178114	−	0.102834i	−0.408292	−	0.912851i	$-0.633875\pi$
$79$	1.58312	−	0.914012i	0.178114	−	0.102834i	0.586406	+	0.810017i	$0.300542\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	−11.2105	−	11.2105i	−1.23051	−	1.23051i	−0.963769	−	0.266738i	$-0.914054\pi$
$83$	−11.2105	−	11.2105i	−1.23051	−	1.23051i	−0.266738	−	0.963769i	$-0.585946\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.90835	+	6.76946i	0.414284	+	0.717562i	0.995353	−	0.0962928i	$-0.0306985\pi$
$89$	3.90835	+	6.76946i	0.414284	+	0.717562i	−0.581069	+	0.813855i	$0.697365\pi$
$90$		0			0
$91$	−5.16475	+	15.5233i	−0.541413	+	1.62728i
$92$		0			0
$93$	4.37357	+	1.17190i	0.453518	+	0.121520i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.53553	+	3.53553i	−0.358979	+	0.358979i	−0.863437	−	0.504457i	$-0.831693\pi$
$97$	−3.53553	+	3.53553i	−0.358979	+	0.358979i	0.504457	+	0.863437i	$0.331693\pi$
$98$		0			0
$99$			4.51298i			0.453571i
$100$		0			0
$101$	−6.08451	−	3.51290i	−0.605432	−	0.349546i	0.165744	−	0.986169i	$-0.446998\pi$
$101$	−6.08451	−	3.51290i	−0.605432	−	0.349546i	−0.771175	+	0.636623i	$0.780331\pi$
$102$		0			0
$103$	−1.07979	+	4.02982i	−0.106395	+	0.397070i	−0.998500	−	0.0547581i	$-0.982561\pi$
$103$	−1.07979	+	4.02982i	−0.106395	+	0.397070i	0.892105	+	0.451828i	$0.149228\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.81841	−	6.78639i	0.175792	−	0.656065i	−0.820623	−	0.571470i	$-0.806373\pi$
$107$	1.81841	−	6.78639i	0.175792	−	0.656065i	0.996415	−	0.0845956i	$-0.0269598\pi$
$108$		0			0
$109$	11.7125	+	6.76224i	1.12186	+	0.647705i	0.941875	−	0.335965i	$-0.109062\pi$
$109$	11.7125	+	6.76224i	1.12186	+	0.647705i	0.179983	+	0.983670i	$0.442396\pi$
$110$		0			0
$111$			1.73205i			0.164399i
$112$		0			0
$113$	−7.34847	+	7.34847i	−0.691286	+	0.691286i	−0.962515	−	0.271229i	$-0.912570\pi$
$113$	−7.34847	+	7.34847i	−0.691286	+	0.691286i	0.271229	+	0.962515i	$0.412570\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.97278	−	1.60040i	−0.552184	−	0.147957i
$118$		0			0
$119$	8.92925	−	7.92699i	0.818543	−	0.726666i
$120$		0			0
$121$	−4.68348	−	8.11202i	−0.425771	−	0.737456i
$122$		0			0
$123$	0.575897	+	2.14928i	0.0519269	+	0.193794i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	10.7059	+	10.7059i	0.949991	+	0.949991i	0.998808	−	0.0488168i	$-0.0155451\pi$
$127$	10.7059	+	10.7059i	0.949991	+	0.949991i	−0.0488168	+	0.998808i	$0.515545\pi$
$128$		0			0
$129$	−5.55278	+	9.61769i	−0.488895	+	0.846790i
$130$		0			0
$131$	12.8540	−	7.42125i	1.12306	−	0.648397i	0.180878	−	0.983506i	$-0.442106\pi$
$131$	12.8540	−	7.42125i	1.12306	−	0.648397i	0.942180	+	0.335108i	$0.108773\pi$
$132$		0			0
$133$	7.31315	−	11.0898i	0.634131	−	0.961608i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.10253	+	0.295421i	−0.0941953	+	0.0252395i	−0.305609	−	0.952157i	$-0.598860\pi$
$137$	−1.10253	+	0.295421i	−0.0941953	+	0.0252395i	0.211414	+	0.977397i	$0.432193\pi$
$138$		0			0
$139$	20.5766			1.74529			0.872644	−	0.488357i	$-0.162404\pi$
$139$	20.5766			1.74529			0.872644	+	0.488357i	$0.162404\pi$
$140$		0			0
$141$	−12.8799			−1.08469
$142$		0			0
$143$	26.9550	−	7.22257i	2.25409	−	0.603982i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.60020	−	6.49915i	0.214461	−	0.536041i
$148$		0			0
$149$	16.9212	−	9.76946i	1.38624	−	0.800346i	0.393350	−	0.919389i	$-0.371316\pi$
$149$	16.9212	−	9.76946i	1.38624	−	0.800346i	0.992889	+	0.119043i	$0.0379826\pi$
$150$		0			0
$151$	5.75649	−	9.97053i	0.468456	−	0.811390i	−0.530894	−	0.847438i	$-0.678144\pi$
$151$	5.75649	−	9.97053i	0.468456	−	0.811390i	0.999350	+	0.0360482i	$0.0114770\pi$
$152$		0			0
$153$	3.19116	+	3.19116i	0.257990	+	0.257990i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−2.07727	−	7.75247i	−0.165784	−	0.618715i	−0.997939	−	0.0641713i	$-0.979560\pi$
$157$	−2.07727	−	7.75247i	−0.165784	−	0.618715i	0.832155	−	0.554543i	$-0.187107\pi$
$158$		0			0
$159$	6.13345	+	10.6234i	0.486414	+	0.842494i
$160$		0			0
$161$	−2.97405	−	14.4920i	−0.234388	−	1.14213i
$162$		0			0
$163$	4.16087	+	1.11490i	0.325905	+	0.0873259i	0.418062	−	0.908419i	$-0.362710\pi$
$163$	4.16087	+	1.11490i	0.325905	+	0.0873259i	−0.0921571	+	0.995744i	$0.529376\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.119519	−	0.119519i	0.00924866	−	0.00924866i	−0.702467	−	0.711716i	$-0.747918\pi$
$167$	0.119519	−	0.119519i	0.00924866	−	0.00924866i	0.711716	+	0.702467i	$0.247918\pi$
$168$		0			0
$169$			25.2354i			1.94118i
$170$		0			0
$171$	4.34823	+	2.51045i	0.332517	+	0.191979i
$172$		0			0
$173$	3.88900	−	14.5140i	0.295675	−	1.10348i	−0.645004	−	0.764179i	$-0.723144\pi$
$173$	3.88900	−	14.5140i	0.295675	−	1.10348i	0.940679	−	0.339296i	$-0.110189\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.575897	+	2.14928i	−0.0432871	+	0.161549i
$178$		0			0
$179$	−17.0676	−	9.85398i	−1.27569	−	0.736521i	−0.299638	−	0.954053i	$-0.596866\pi$
$179$	−17.0676	−	9.85398i	−1.27569	−	0.736521i	−0.976053	+	0.217532i	$0.930199\pi$
$180$		0			0
$181$			9.32855i			0.693386i	0.937979	+	0.346693i	$0.112695\pi$
$181$			9.32855i			0.693386i	−0.937979	+	0.346693i	$0.887305\pi$
$182$		0			0
$183$	−5.17861	+	5.17861i	−0.382814	+	0.382814i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−19.6730	−	5.27136i	−1.43863	−	0.385480i
$188$		0			0
$189$	2.51045	+	0.835250i	0.182608	+	0.0607555i
$190$		0			0
$191$	7.95294	+	13.7749i	0.575455	+	0.996717i	0.995992	+	0.0894414i	$0.0285082\pi$
$191$	7.95294	+	13.7749i	0.575455	+	0.996717i	−0.420538	+	0.907275i	$0.638158\pi$
$192$		0			0
$193$	1.17190	+	4.37357i	0.0843549	+	0.314817i	0.995191	−	0.0979510i	$-0.0312288\pi$
$193$	1.17190	+	4.37357i	0.0843549	+	0.314817i	−0.910836	+	0.412768i	$0.864562\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.5959	+	17.5959i	1.25365	+	1.25365i	0.954071	+	0.299582i	$0.0968472\pi$
$197$	17.5959	+	17.5959i	1.25365	+	1.25365i	0.299582	+	0.954071i	$0.403153\pi$
$198$		0			0
$199$	−4.59912	+	7.96592i	−0.326023	+	0.564689i	−0.981719	−	0.190336i	$-0.939042\pi$
$199$	−4.59912	+	7.96592i	−0.326023	+	0.564689i	0.655696	+	0.755025i	$0.272375\pi$
$200$		0			0
$201$	−4.34823	+	2.51045i	−0.306700	+	0.177073i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	5.40108	−	1.44721i	0.375401	−	0.100588i
$208$		0			0
$209$	−22.6592			−1.56737
$210$		0			0
$211$	3.14602			0.216581			0.108291	−	0.994119i	$-0.465462\pi$
$211$	3.14602			0.216581			0.108291	+	0.994119i	$0.465462\pi$
$212$		0			0
$213$	−13.8774	+	3.71844i	−0.950865	+	0.254783i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.711043	+	11.9585i	−0.0482688	+	0.811793i
$218$		0			0
$219$	3.75942	−	2.17050i	0.254038	−	0.146669i
$220$		0			0
$221$	13.9529	−	24.1672i	0.938576	−	1.62566i
$222$		0			0
$223$	−6.46722	−	6.46722i	−0.433077	−	0.433077i	0.456597	−	0.889674i	$-0.349068\pi$
$223$	−6.46722	−	6.46722i	−0.433077	−	0.433077i	−0.889674	+	0.456597i	$0.849068\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.05956	+	15.1505i	0.269443	+	1.00557i	0.959475	+	0.281795i	$0.0909298\pi$
$227$	4.05956	+	15.1505i	0.269443	+	1.00557i	−0.690032	+	0.723779i	$0.742404\pi$
$228$		0			0
$229$	−9.21461	−	15.9602i	−0.608918	−	1.05468i	−0.991419	−	0.130722i	$-0.958270\pi$
$229$	−9.21461	−	15.9602i	−0.608918	−	1.05468i	0.382501	−	0.923955i	$-0.375063\pi$
$230$		0			0
$231$	−11.6965	+	2.40035i	−0.769570	+	0.157931i
$232$		0			0
$233$	2.48784	+	0.666615i	0.162984	+	0.0436714i	0.339388	−	0.940646i	$-0.389780\pi$
$233$	2.48784	+	0.666615i	0.162984	+	0.0436714i	−0.176404	+	0.984318i	$0.556447\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.29261	+	1.29261i	−0.0839640	+	0.0839640i
$238$		0			0
$239$			0.607095i			0.0392697i	0.999807	+	0.0196349i	$0.00625037\pi$
$239$			0.607095i			0.0392697i	−0.999807	+	0.0196349i	$0.993750\pi$
$240$		0			0
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	0.238597	−	0.971119i	$-0.423312\pi$
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	−0.721715	+	0.692191i	$0.756646\pi$
$242$		0			0
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.03545	−	29.9887i	0.511284	−	1.90814i
$248$		0			0
$249$	13.7299	+	7.92699i	0.870100	+	0.502352i
$250$		0			0
$251$			28.2508i			1.78318i	0.452848	+	0.891588i	$0.350408\pi$
$251$			28.2508i			1.78318i	−0.452848	+	0.891588i	$0.649592\pi$
$252$		0			0
$253$	−17.8437	+	17.8437i	−1.12182	+	1.12182i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.99574	−	1.33861i	−0.311626	−	0.0834999i	0.0996165	−	0.995026i	$-0.468238\pi$
$257$	−4.99574	−	1.33861i	−0.311626	−	0.0834999i	−0.411243	+	0.911526i	$0.634905\pi$
$258$		0			0
$259$	−4.48902	+	0.921238i	−0.278934	+	0.0572429i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.13694	+	15.4393i	0.255095	+	0.952027i	0.968038	+	0.250805i	$0.0806951\pi$
$263$	4.13694	+	15.4393i	0.255095	+	0.952027i	−0.712943	+	0.701222i	$0.752638\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.52724	−	5.52724i	−0.338262	−	0.338262i
$268$		0			0
$269$	8.75400	−	15.1624i	0.533741	−	0.924466i	−0.465483	−	0.885057i	$-0.654119\pi$
$269$	8.75400	−	15.1624i	0.533741	−	0.924466i	0.999223	−	0.0394089i	$-0.0125475\pi$
$270$		0			0
$271$	−9.38140	+	5.41636i	−0.569880	+	0.329020i	−0.757101	−	0.653298i	$-0.773385\pi$
$271$	−9.38140	+	5.41636i	−0.569880	+	0.329020i	0.187222	+	0.982318i	$0.440052\pi$
$272$		0			0
$273$	0.971038	−	16.3311i	0.0587699	−	0.988403i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−11.2976	+	3.02719i	−0.678810	+	0.181887i	−0.581720	−	0.813389i	$-0.697620\pi$
$277$	−11.2976	+	3.02719i	−0.678810	+	0.181887i	−0.0970897	+	0.995276i	$0.530953\pi$
$278$		0			0
$279$	−4.52786			−0.271076
$280$		0			0
$281$	25.5389			1.52352			0.761762	−	0.647857i	$-0.224334\pi$
$281$	25.5389			1.52352			0.761762	+	0.647857i	$0.224334\pi$
$282$		0			0
$283$	−16.4598	+	4.41038i	−0.978431	+	0.262170i	−0.712384	−	0.701790i	$-0.752384\pi$
$283$	−16.4598	+	4.41038i	−0.978431	+	0.262170i	−0.266048	+	0.963960i	$0.585718\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.26406	+	2.63572i	−0.310727	+	0.155582i
$288$		0			0
$289$	−2.91587	+	1.68348i	−0.171522	+	0.0990280i
$290$		0			0
$291$	2.50000	−	4.33013i	0.146553	−	0.253837i
$292$		0			0
$293$	−0.429281	−	0.429281i	−0.0250789	−	0.0250789i	0.694456	−	0.719535i	$-0.255645\pi$
$293$	−0.429281	−	0.429281i	−0.0250789	−	0.0250789i	−0.719535	+	0.694456i	$0.755645\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.16804	−	4.35920i	−0.0677768	−	0.252946i
$298$		0			0
$299$	−17.2878	−	29.9433i	−0.999779	−	1.73167i
$300$		0			0
$301$	−27.8799	−	9.27591i	−1.60697	−	0.534655i
$302$		0			0
$303$	6.78639	+	1.81841i	0.389868	+	0.104465i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	11.2390	−	11.2390i	0.641445	−	0.641445i	−0.309466	−	0.950911i	$-0.600150\pi$
$307$	11.2390	−	11.2390i	0.641445	−	0.641445i	0.950911	+	0.309466i	$0.100150\pi$
$308$		0			0
$309$		−	4.17198i		−	0.237335i
$310$		0			0
$311$	−0.988499	−	0.570710i	−0.0560526	−	0.0323620i	0.471712	−	0.881753i	$-0.343636\pi$
$311$	−0.988499	−	0.570710i	−0.0560526	−	0.0323620i	−0.527764	+	0.849391i	$0.676970\pi$
$312$		0			0
$313$	1.16507	−	4.34809i	0.0658535	−	0.245769i	−0.925151	−	0.379600i	$-0.876061\pi$
$313$	1.16507	−	4.34809i	0.0658535	−	0.245769i	0.991004	+	0.133832i	$0.0427282\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.50829	+	9.36107i	−0.140880	+	0.525770i	0.859025	+	0.511934i	$0.171071\pi$
$317$	−2.50829	+	9.36107i	−0.140880	+	0.525770i	−0.999904	+	0.0138358i	$0.995596\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$			7.02579i			0.392141i
$322$		0			0
$323$	−16.0225	+	16.0225i	−0.891514	+	0.891514i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−13.0636	−	3.50039i	−0.722421	−	0.193572i
$328$		0			0
$329$	−6.85054	−	33.3814i	−0.377682	−	1.84038i
$330$		0			0
$331$	−1.90251	−	3.29525i	−0.104571	−	0.181123i	0.808992	−	0.587820i	$-0.200014\pi$
$331$	−1.90251	−	3.29525i	−0.104571	−	0.181123i	−0.913563	+	0.406697i	$0.866680\pi$
$332$		0			0
$333$	−0.448288	−	1.67303i	−0.0245660	−	0.0916816i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−10.8616	−	10.8616i	−0.591667	−	0.591667i	0.346415	−	0.938082i	$-0.387399\pi$
$337$	−10.8616	−	10.8616i	−0.591667	−	0.591667i	−0.938082	+	0.346415i	$0.887399\pi$
$338$		0			0
$339$	5.19615	−	9.00000i	0.282216	−	0.488813i
$340$		0			0
$341$	17.6965	−	10.2171i	0.958317	−	0.553284i
$342$		0			0
$343$	18.2271	+	3.28230i	0.984170	+	0.177227i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12.9514	−	3.47033i	0.695270	−	0.186297i	0.106159	−	0.994349i	$-0.466145\pi$
$347$	12.9514	−	3.47033i	0.695270	−	0.186297i	0.589111	+	0.808052i	$0.299478\pi$
$348$		0			0
$349$	−35.2766			−1.88831			−0.944156	−	0.329497i	$-0.893121\pi$
$349$	−35.2766			−1.88831			−0.944156	+	0.329497i	$0.893121\pi$
$350$		0			0
$351$	6.18348			0.330050
$352$		0			0
$353$	4.30906	−	1.15461i	0.229348	−	0.0614537i	−0.142314	−	0.989821i	$-0.545454\pi$
$353$	4.30906	−	1.15461i	0.229348	−	0.0614537i	0.371663	+	0.928368i	$0.378788\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−6.57334	+	9.96794i	−0.347898	+	0.527559i
$358$		0			0
$359$	−10.0129	+	5.78097i	−0.528462	+	0.305108i	−0.740390	−	0.672178i	$-0.765359\pi$
$359$	−10.0129	+	5.78097i	−0.528462	+	0.305108i	0.211928	+	0.977285i	$0.432026\pi$
$360$		0			0
$361$	−3.10471	+	5.37752i	−0.163406	+	0.283028i
$362$		0			0
$363$	6.62344	+	6.62344i	0.347640	+	0.347640i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.728970	+	2.72055i	0.0380519	+	0.142012i	0.982338	−	0.187113i	$-0.0599130\pi$
$367$	0.728970	+	2.72055i	0.0380519	+	0.142012i	−0.944286	+	0.329125i	$0.893246\pi$
$368$		0			0
$369$	−1.11255	−	1.92699i	−0.0579169	−	0.100315i
$370$		0			0
$371$	−24.2709	+	21.5467i	−1.26008	+	1.11865i
$372$		0			0
$373$	22.7769	+	6.10306i	1.17934	+	0.316004i	0.794667	−	0.607046i	$-0.207646\pi$
$373$	22.7769	+	6.10306i	1.17934	+	0.316004i	0.384678	+	0.923051i	$0.374312\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$			12.6445i			0.649507i	0.945799	+	0.324753i	$0.105281\pi$
$379$			12.6445i			0.649507i	−0.945799	+	0.324753i	$0.894719\pi$
$380$		0			0
$381$	−13.1119	−	7.57018i	−0.671745	−	0.387832i
$382$		0			0
$383$	2.16553	−	8.08186i	0.110653	−	0.412964i	−0.888272	−	0.459318i	$-0.848094\pi$
$383$	2.16553	−	8.08186i	0.110653	−	0.412964i	0.998925	+	0.0463547i	$0.0147604\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.87433	−	10.7271i	0.146110	−	0.545291i
$388$		0			0
$389$	−4.77182	−	2.75501i	−0.241941	−	0.139685i	0.374128	−	0.927377i	$-0.377942\pi$
$389$	−4.77182	−	2.75501i	−0.241941	−	0.139685i	−0.616069	+	0.787693i	$0.711276\pi$
$390$		0			0
$391$			25.2348i			1.27618i
$392$		0			0
$393$	−10.4952	+	10.4952i	−0.529414	+	0.529414i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−20.5118	−	5.49612i	−1.02946	−	0.275842i	−0.295720	−	0.955275i	$-0.595559\pi$
$397$	−20.5118	−	5.49612i	−1.02946	−	0.275842i	−0.733738	+	0.679432i	$0.762226\pi$
$398$		0			0
$399$	−4.19371	+	12.6047i	−0.209948	+	0.631025i
$400$		0			0
$401$	−7.26799	−	12.5885i	−0.362946	−	0.628641i	0.625498	−	0.780226i	$-0.284896\pi$
$401$	−7.26799	−	12.5885i	−0.362946	−	0.628641i	−0.988444	+	0.151585i	$0.951562\pi$
$402$		0			0
$403$	7.24639	+	27.0439i	0.360968	+	1.34715i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.52724	+	5.52724i	0.273975	+	0.273975i
$408$		0			0
$409$	9.21461	−	15.9602i	0.455633	−	0.789179i	−0.543091	−	0.839674i	$-0.682746\pi$
$409$	9.21461	−	15.9602i	0.455633	−	0.789179i	0.998724	+	0.0504942i	$0.0160796\pi$
$410$		0			0
$411$	0.988499	−	0.570710i	0.0487591	−	0.0281511i
$412$		0			0
$413$	−5.87667	−	0.349423i	−0.289172	−	0.0171940i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−19.8755	+	5.32563i	−0.973308	+	0.260797i
$418$		0			0
$419$	9.74904			0.476272			0.238136	−	0.971232i	$-0.423464\pi$
$419$	9.74904			0.476272			0.238136	+	0.971232i	$0.423464\pi$
$420$		0			0
$421$	10.6330			0.518223			0.259112	−	0.965847i	$-0.416570\pi$
$421$	10.6330			0.518223			0.259112	+	0.965847i	$0.416570\pi$
$422$		0			0
$423$	12.4411	−	3.33357i	0.604905	−	0.162084i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−16.1760	−	10.6672i	−0.782811	−	0.516223i
$428$		0			0
$429$	−24.1672	+	13.9529i	−1.16680	+	0.673654i
$430$		0			0
$431$	−16.2354	+	28.1205i	−0.782031	+	1.35452i	0.148726	+	0.988878i	$0.452483\pi$
$431$	−16.2354	+	28.1205i	−0.782031	+	1.35452i	−0.930757	+	0.365639i	$0.880851\pi$
$432$		0			0
$433$	−23.2782	−	23.2782i	−1.11868	−	1.11868i	−0.991936	−	0.126743i	$-0.959548\pi$
$433$	−23.2782	−	23.2782i	−1.11868	−	1.11868i	−0.126743	−	0.991936i	$-0.540452\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	7.26632	+	27.1183i	0.347595	+	1.29724i
$438$		0			0
$439$	6.99947	+	12.1234i	0.334067	+	0.578620i	0.983305	−	0.181965i	$-0.0582456\pi$
$439$	6.99947	+	12.1234i	0.334067	+	0.578620i	−0.649239	+	0.760585i	$0.724912\pi$
$440$		0			0
$441$	−0.829500	+	6.95068i	−0.0395000	+	0.330985i
$442$		0			0
$443$	−0.763964	−	0.204704i	−0.0362970	−	0.00972576i	0.240625	−	0.970618i	$-0.422648\pi$
$443$	−0.763964	−	0.204704i	−0.0362970	−	0.00972576i	−0.276922	+	0.960892i	$0.589314\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−13.8161	+	13.8161i	−0.653480	+	0.653480i
$448$		0			0
$449$		−	15.9059i		−	0.750645i	−0.926894	−	0.375322i	$-0.877532\pi$
$449$		−	15.9059i		−	0.750645i	0.926894	−	0.375322i	$-0.122468\pi$
$450$		0			0
$451$	8.69645	+	5.02090i	0.409500	+	0.236425i
$452$		0			0
$453$	−2.97978	+	11.1207i	−0.140002	+	0.522495i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.48783	+	35.4090i	−0.443822	+	1.65637i	0.275207	+	0.961385i	$0.411254\pi$
$457$	−9.48783	+	35.4090i	−0.443822	+	1.65637i	−0.719029	+	0.694980i	$0.755413\pi$
$458$		0			0
$459$	−3.90835	−	2.25649i	−0.182426	−	0.105324i
$460$		0			0
$461$		−	14.1415i		−	0.658634i	−0.944219	−	0.329317i	$-0.893181\pi$
$461$		−	14.1415i		−	0.658634i	0.944219	−	0.329317i	$-0.106819\pi$
$462$		0			0
$463$	−16.4119	+	16.4119i	−0.762728	+	0.762728i	−0.976815	−	0.214087i	$-0.931322\pi$
$463$	−16.4119	+	16.4119i	−0.762728	+	0.762728i	0.214087	+	0.976815i	$0.431322\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	23.2324	+	6.22509i	1.07507	+	0.288063i	0.752573	−	0.658509i	$-0.228813\pi$
$467$	23.2324	+	6.22509i	1.07507	+	0.288063i	0.322492	+	0.946572i	$0.395479\pi$
$468$		0			0
$469$	−8.81915	−	9.93421i	−0.407230	−	0.458719i
$470$		0			0
$471$	4.01298	+	6.95068i	0.184908	+	0.320270i
$472$		0			0
$473$	12.9718	+	48.4113i	0.596443	+	2.22596i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−8.67400	−	8.67400i	−0.397155	−	0.397155i
$478$		0			0
$479$	−0.146380	+	0.253538i	−0.00668829	+	0.0115845i	−0.869350	−	0.494197i	$-0.835462\pi$
$479$	−0.146380	+	0.253538i	−0.00668829	+	0.0115845i	0.862662	+	0.505781i	$0.168796\pi$
$480$		0			0
$481$	−9.27521	+	5.35505i	−0.422913	+	0.244169i
$482$		0			0
$483$	6.62351	+	13.2284i	0.301380	+	0.601915i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−4.03501	+	1.08118i	−0.182844	+	0.0489928i	−0.349079	−	0.937093i	$-0.613506\pi$
$487$	−4.03501	+	1.08118i	−0.182844	+	0.0489928i	0.166235	+	0.986086i	$0.446839\pi$
$488$		0			0
$489$	−4.30765			−0.194799
$490$		0			0
$491$	5.28910			0.238694			0.119347	−	0.992853i	$-0.461920\pi$
$491$	5.28910			0.238694			0.119347	+	0.992853i	$0.461920\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.0183	−	33.9889i	−0.763375	−	1.52461i
$498$		0			0
$499$	25.4675	−	14.7037i	1.14008	−	0.658227i	0.193632	−	0.981074i	$-0.437973\pi$
$499$	25.4675	−	14.7037i	1.14008	−	0.658227i	0.946451	+	0.322847i	$0.104640\pi$
$500$		0			0
$501$	−0.0845127	+	0.146380i	−0.00377575	+	0.00653979i
$502$		0			0
$503$	−25.4558	−	25.4558i	−1.13502	−	1.13502i	−0.989330	−	0.145690i	$-0.953460\pi$
$503$	−25.4558	−	25.4558i	−1.13502	−	1.13502i	−0.145690	−	0.989330i	$-0.546540\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.53140	−	24.3755i	−0.290070	−	1.08255i
$508$		0			0
$509$	5.76686	+	9.98850i	0.255612	+	0.442732i	0.965061	−	0.262024i	$-0.0843898\pi$
$509$	5.76686	+	9.98850i	0.255612	+	0.442732i	−0.709450	+	0.704756i	$0.751056\pi$
$510$		0			0
$511$	7.62492	+	8.58899i	0.337306	+	0.379954i
$512$		0			0
$513$	−4.84982	−	1.29950i	−0.214125	−	0.0573745i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−41.1019	+	41.1019i	−1.80766	+	1.80766i
$518$		0			0
$519$			15.0260i			0.659566i
$520$		0			0
$521$	0.684951	+	0.395457i	0.0300083	+	0.0173253i	0.514929	−	0.857233i	$-0.327818\pi$
$521$	0.684951	+	0.395457i	0.0300083	+	0.0173253i	−0.484921	+	0.874558i	$0.661152\pi$
$522$		0			0
$523$	−9.64318	+	35.9888i	−0.421667	+	1.57368i	0.349429	+	0.936963i	$0.386376\pi$
$523$	−9.64318	+	35.9888i	−0.421667	+	1.57368i	−0.771096	+	0.636719i	$0.780291\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.28874	−	19.7378i	0.230381	−	0.859793i
$528$		0			0
$529$	7.15865	+	4.13305i	0.311246	+	0.179698i
$530$		0			0
$531$		−	2.22509i		−	0.0965609i
$532$		0			0
$533$	−9.72895	+	9.72895i	−0.421408	+	0.421408i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	19.0364	+	5.10079i	0.821482	+	0.220115i
$538$		0			0
$539$	−12.4421	−	29.0375i	−0.535921	−	1.25073i
$540$		0			0
$541$	−1.05429	−	1.82608i	−0.0453273	−	0.0785091i	0.842472	−	0.538741i	$-0.181100\pi$
$541$	−1.05429	−	1.82608i	−0.0453273	−	0.0785091i	−0.887799	+	0.460232i	$0.847766\pi$
$542$		0			0
$543$	−2.41441	−	9.01069i	−0.103612	−	0.386686i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−20.7426	−	20.7426i	−0.886890	−	0.886890i	0.107333	−	0.994223i	$-0.465769\pi$
$547$	−20.7426	−	20.7426i	−0.886890	−	0.886890i	−0.994223	+	0.107333i	$0.965769\pi$
$548$		0			0
$549$	3.66183	−	6.34248i	0.156283	−	0.270690i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−4.03761	−	2.66259i	−0.171697	−	0.113225i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.1407	+	2.98515i	−0.472048	+	0.126485i	−0.486997	−	0.873403i	$-0.661908\pi$
$557$	−11.1407	+	2.98515i	−0.472048	+	0.126485i	0.0149497	+	0.999888i	$0.495241\pi$
$558$		0			0
$559$	−68.6709			−2.90447
$560$		0			0
$561$	20.3670			0.859893
$562$		0			0
$563$	−6.05909	+	1.62353i	−0.255360	+	0.0684236i	−0.384228	−	0.923238i	$-0.625532\pi$
$563$	−6.05909	+	1.62353i	−0.255360	+	0.0684236i	0.128868	+	0.991662i	$0.458866\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.64109	−	0.157038i	−0.110915	−	0.00659496i
$568$		0			0
$569$	26.1721	−	15.1105i	1.09719	−	0.633464i	0.161709	−	0.986838i	$-0.448299\pi$
$569$	26.1721	−	15.1105i	1.09719	−	0.633464i	0.935482	+	0.353375i	$0.114966\pi$
$570$		0			0
$571$	18.7037	−	32.3957i	0.782725	−	1.35572i	−0.147624	−	0.989043i	$-0.547163\pi$
$571$	18.7037	−	32.3957i	0.782725	−	1.35572i	0.930349	−	0.366675i	$-0.119504\pi$
$572$		0			0
$573$	−11.2472	−	11.2472i	−0.469857	−	0.469857i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−4.78853	−	17.8711i	−0.199349	−	0.743982i	−0.991098	−	0.133135i	$-0.957496\pi$
$577$	−4.78853	−	17.8711i	−0.199349	−	0.743982i	0.791749	−	0.610847i	$-0.209171\pi$
$578$		0			0
$579$	−2.26393	−	3.92124i	−0.0940856	−	0.162961i
$580$		0			0
$581$	−13.2420	+	39.8006i	−0.549372	+	1.65121i
$582$		0			0
$583$	53.4738	+	14.3283i	2.21466	+	0.593416i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.17461	−	5.17461i	0.213579	−	0.213579i	−0.592207	−	0.805786i	$-0.701743\pi$
$587$	5.17461	−	5.17461i	0.213579	−	0.213579i	0.805786	+	0.592207i	$0.201743\pi$
$588$		0			0
$589$		−	22.7339i		−	0.936734i
$590$		0			0
$591$	−21.5504	−	12.4421i	−0.886466	−	0.511802i
$592$		0			0
$593$	−10.7401	+	40.0827i	−0.441045	+	1.64600i	0.285128	+	0.958489i	$0.407964\pi$
$593$	−10.7401	+	40.0827i	−0.441045	+	1.64600i	−0.726173	+	0.687512i	$0.758703\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.38068	−	8.88483i	0.0974348	−	0.363632i
$598$		0			0
$599$	−36.2716	−	20.9414i	−1.48202	−	0.855644i	−0.482227	−	0.876046i	$-0.660172\pi$
$599$	−36.2716	−	20.9414i	−1.48202	−	0.855644i	−0.999792	+	0.0204023i	$0.993505\pi$
$600$		0			0
$601$			3.49682i			0.142638i	0.997454	+	0.0713191i	$0.0227209\pi$
$601$			3.49682i			0.142638i	−0.997454	+	0.0713191i	$0.977279\pi$
$602$		0			0
$603$	3.55031	−	3.55031i	0.144580	−	0.144580i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	16.9664	+	4.54613i	0.688644	+	0.184522i	0.586138	−	0.810211i	$-0.300647\pi$
$607$	16.9664	+	4.54613i	0.688644	+	0.184522i	0.102505	+	0.994732i	$0.467314\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−39.8214	−	68.9726i	−1.61100	−	2.79033i
$612$		0			0
$613$	−9.53966	−	35.6025i	−0.385303	−	1.43797i	−0.837688	−	0.546149i	$-0.816093\pi$
$613$	−9.53966	−	35.6025i	−0.385303	−	1.43797i	0.452385	−	0.891823i	$-0.350573\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.3023	+	11.3023i	0.455015	+	0.455015i	0.897015	−	0.442000i	$-0.145731\pi$
$617$	11.3023	+	11.3023i	0.455015	+	0.455015i	−0.442000	+	0.897015i	$0.645731\pi$
$618$		0			0
$619$	22.7956	−	39.4832i	0.916233	−	1.58696i	0.111148	−	0.993804i	$-0.464547\pi$
$619$	22.7956	−	39.4832i	0.916233	−	1.58696i	0.805086	−	0.593159i	$-0.202119\pi$
$620$		0			0
$621$	−4.84248	+	2.79580i	−0.194322	+	0.112192i
$622$		0			0
$623$	11.3854	−	17.2650i	0.456145	−	0.691707i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	21.8871	−	5.86463i	0.874087	−	0.234211i
$628$		0			0
$629$	7.81670			0.311672
$630$		0			0
$631$	33.9029			1.34965			0.674827	−	0.737976i	$-0.264218\pi$
$631$	33.9029			1.34965			0.674827	+	0.737976i	$0.264218\pi$
$632$		0			0
$633$	−3.03883	+	0.814251i	−0.120782	+	0.0323636i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	42.8424	−	6.16946i	1.69748	−	0.244443i
$638$		0			0
$639$	12.4421	−	7.18348i	0.492204	−	0.284174i
$640$		0			0
$641$	20.0634	−	34.7508i	0.792457	−	1.37258i	−0.131985	−	0.991252i	$-0.542135\pi$
$641$	20.0634	−	34.7508i	0.792457	−	1.37258i	0.924442	−	0.381324i	$-0.124532\pi$
$642$		0			0
$643$	18.5960	+	18.5960i	0.733357	+	0.733357i	0.971283	−	0.237927i	$-0.0764678\pi$
$643$	18.5960	+	18.5960i	0.733357	+	0.733357i	−0.237927	+	0.971283i	$0.576468\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.73439	−	10.2049i	−0.107500	−	0.401196i	0.891117	−	0.453774i	$-0.149923\pi$
$647$	−2.73439	−	10.2049i	−0.107500	−	0.401196i	−0.998617	+	0.0525785i	$0.983256\pi$
$648$		0			0
$649$	5.02090	+	8.69645i	0.197088	+	0.341366i
$650$		0			0
$651$	−2.40826	−	11.7350i	−0.0943872	−	0.459932i
$652$		0			0
$653$	41.6249	+	11.1534i	1.62891	+	0.436465i	0.953602	−	0.301071i	$-0.0973441\pi$
$653$	41.6249	+	11.1534i	1.62891	+	0.436465i	0.675308	+	0.737536i	$0.264011\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−3.06955	+	3.06955i	−0.119755	+	0.119755i
$658$		0			0
$659$			10.4611i			0.407506i	0.979022	+	0.203753i	$0.0653139\pi$
$659$			10.4611i			0.407506i	−0.979022	+	0.203753i	$0.934686\pi$
$660$		0			0
$661$	−36.7584	−	21.2225i	−1.42974	−	0.825458i	−0.432636	−	0.901569i	$-0.642416\pi$
$661$	−36.7584	−	21.2225i	−1.42974	−	0.825458i	−0.997099	+	0.0761106i	$0.975750\pi$
$662$		0			0
$663$	−7.22257	+	26.9550i	−0.280502	+	1.04685i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	7.92069	+	4.57301i	0.306232	+	0.176803i
$670$		0			0
$671$			33.0515i			1.27594i
$672$		0			0
$673$	−23.0223	+	23.0223i	−0.887445	+	0.887445i	−0.994277	−	0.106832i	$-0.965929\pi$
$673$	−23.0223	+	23.0223i	−0.887445	+	0.887445i	0.106832	+	0.994277i	$0.465929\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.20915	−	1.39579i	−0.200204	−	0.0536444i	0.157324	−	0.987547i	$-0.449713\pi$
$677$	−5.20915	−	1.39579i	−0.200204	−	0.0536444i	−0.357527	+	0.933903i	$0.616380\pi$
$678$		0			0
$679$	12.5522	+	4.17625i	0.481711	+	0.160270i
$680$		0			0
$681$	−7.84248	−	13.5836i	−0.300524	−	0.520523i
$682$		0			0
$683$	9.88759	+	36.9010i	0.378338	+	1.41198i	0.848406	+	0.529346i	$0.177563\pi$
$683$	9.88759	+	36.9010i	0.378338	+	1.41198i	−0.470068	+	0.882630i	$0.655771\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	13.0314	+	13.0314i	0.497180	+	0.497180i
$688$		0			0
$689$	−37.9260	+	65.6898i	−1.44487	+	2.50258i
$690$		0			0
$691$	−4.58451	+	2.64687i	−0.174403	+	0.100692i	−0.584660	−	0.811278i	$-0.698772\pi$
$691$	−4.58451	+	2.64687i	−0.174403	+	0.100692i	0.410257	+	0.911970i	$0.365439\pi$
$692$		0			0
$693$	10.6766	−	5.34582i	0.405572	−	0.203071i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.69963	−	2.59901i	0.367400	−	0.0984445i
$698$		0			0
$699$	−2.57560			−0.0974182
$700$		0			0
$701$	17.8310			0.673467			0.336733	−	0.941600i	$-0.390678\pi$
$701$	17.8310			0.673467			0.336733	+	0.941600i	$0.390678\pi$
$702$		0			0
$703$	8.40013	−	2.25081i	0.316817	−	0.0848908i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.10331	+	18.5557i	−0.0414944	+	0.697860i
$708$		0			0
$709$	6.63289	−	3.82950i	0.249103	−	0.143820i	−0.370250	−	0.928932i	$-0.620728\pi$
$709$	6.63289	−	3.82950i	0.249103	−	0.143820i	0.619354	+	0.785112i	$0.287395\pi$
$710$		0			0
$711$	0.914012	−	1.58312i	0.0342781	−	0.0593715i
$712$		0			0
$713$	−17.9025	−	17.9025i	−0.670455	−	0.670455i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.157128	−	0.586409i	−0.00586804	−	0.0218998i
$718$		0			0
$719$	6.30870	+	10.9270i	0.235275	+	0.407508i	0.959353	−	0.282210i	$-0.0910677\pi$
$719$	6.30870	+	10.9270i	0.235275	+	0.407508i	−0.724078	+	0.689718i	$0.757734\pi$
$720$		0			0
$721$	10.8127	−	2.21898i	0.402685	−	0.0826390i
$722$		0			0
$723$	8.36516	+	2.24144i	0.311104	+	0.0833600i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	13.4799	−	13.4799i	0.499940	−	0.499940i	−0.411479	−	0.911419i	$-0.634988\pi$
$727$	13.4799	−	13.4799i	0.499940	−	0.499940i	0.911419	+	0.411479i	$0.134988\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	43.4044	+	25.0595i	1.60537	+	0.926861i
$732$		0			0
$733$	−2.32342	+	8.67111i	−0.0858174	+	0.320275i	−0.995468	−	0.0951000i	$-0.969683\pi$
$733$	−2.32342	+	8.67111i	−0.0858174	+	0.320275i	0.909650	+	0.415375i	$0.136350\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.86463	+	21.8871i	−0.216026	+	0.806222i
$738$		0			0
$739$	12.5911	+	7.26946i	0.463170	+	0.267412i	0.713376	−	0.700781i	$-0.247165\pi$
$739$	12.5911	+	7.26946i	0.463170	+	0.267412i	−0.250206	+	0.968193i	$0.580498\pi$
$740$		0			0
$741$			31.0466i			1.14053i
$742$		0			0
$743$	24.4486	−	24.4486i	0.896933	−	0.896933i	−0.0982305	−	0.995164i	$-0.531318\pi$
$743$	24.4486	−	24.4486i	0.896933	−	0.896933i	0.995164	+	0.0982305i	$0.0313182\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−15.3138	−	4.10331i	−0.560301	−	0.150132i
$748$		0			0
$749$	−18.2090	+	3.73686i	−0.665343	+	0.136542i
$750$		0			0
$751$	−21.4644	−	37.1775i	−0.783249	−	1.35663i	−0.930040	−	0.367459i	$-0.880228\pi$
$751$	−21.4644	−	37.1775i	−0.783249	−	1.35663i	0.146791	−	0.989168i	$-0.453105\pi$
$752$		0			0
$753$	−7.31185	−	27.2882i	−0.266459	−	0.994437i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−6.43514	−	6.43514i	−0.233889	−	0.233889i	0.580425	−	0.814314i	$-0.302887\pi$
$757$	−6.43514	−	6.43514i	−0.233889	−	0.233889i	−0.814314	+	0.580425i	$0.802887\pi$
$758$		0			0
$759$	12.6174	−	21.8540i	0.457983	−	0.793249i
$760$		0			0
$761$	12.2969	−	7.09961i	0.445762	−	0.257361i	−0.260277	−	0.965534i	$-0.583814\pi$
$761$	12.2969	−	7.09961i	0.445762	−	0.257361i	0.706039	+	0.708173i	$0.250480\pi$
$762$		0			0
$763$	2.12385	−	35.7193i	0.0768886	−	1.29313i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.2900	+	3.56104i	−0.479874	+	0.128582i
$768$		0			0
$769$	12.7272			0.458955			0.229478	−	0.973314i	$-0.426298\pi$
$769$	12.7272			0.458955			0.229478	+	0.973314i	$0.426298\pi$
$770$		0			0
$771$	5.17198			0.186264
$772$		0			0
$773$	23.1822	−	6.21166i	0.833806	−	0.223418i	0.183433	−	0.983032i	$-0.441279\pi$
$773$	23.1822	−	6.21166i	0.833806	−	0.223418i	0.650374	+	0.759614i	$0.274612\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	4.09763	−	2.05169i	0.147002	−	0.0736040i
$778$		0			0
$779$	9.67521	−	5.58599i	0.346651	−	0.200139i
$780$		0			0
$781$	−32.4189	+	56.1511i	−1.16004	+	2.00924i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1.07231	−	4.00190i	−0.0382236	−	0.142652i	0.944177	−	0.329439i	$-0.106859\pi$
$787$	−1.07231	−	4.00190i	−0.0382236	−	0.142652i	−0.982401	+	0.186786i	$0.940193\pi$
$788$		0			0
$789$	−7.99196	−	13.8425i	−0.284521	−	0.492805i
$790$		0			0
$791$	26.0894	+	8.68017i	0.927631	+	0.308631i
$792$		0			0
$793$	−43.7426	−	11.7208i	−1.55335	−	0.416218i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.2306	+	13.2306i	−0.468652	+	0.468652i	−0.901478	−	0.432826i	$-0.857517\pi$
$797$	−13.2306	+	13.2306i	−0.468652	+	0.468652i	0.432826	+	0.901478i	$0.357517\pi$
$798$		0			0
$799$			58.1268i			2.05638i
$800$		0			0
$801$	6.76946	+	3.90835i	0.239187	+	0.138095i
$802$		0			0
$803$	5.07048	−	18.9233i	0.178933	−	0.667788i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−4.53140	+	16.9114i	−0.159513	+	0.595310i
$808$		0			0
$809$	8.68017	+	5.01150i	0.305179	+	0.176195i	0.644767	−	0.764379i	$-0.276954\pi$
$809$	8.68017	+	5.01150i	0.305179	+	0.176195i	−0.339588	+	0.940574i	$0.610288\pi$
$810$		0			0
$811$			31.1243i			1.09292i	0.837485	+	0.546461i	$0.184025\pi$
$811$			31.1243i			1.09292i	−0.837485	+	0.546461i	$0.815975\pi$
$812$		0			0
$813$	7.65988	−	7.65988i	0.268644	−	0.268644i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	53.8599	+	14.4317i	1.88432	+	0.504902i
$818$		0			0
$819$	3.28885	+	16.0260i	0.114922	+	0.559992i
$820$		0			0
$821$	−6.74351	−	11.6801i	−0.235350	−	0.407638i	0.724024	−	0.689775i	$-0.242290\pi$
$821$	−6.74351	−	11.6801i	−0.235350	−	0.407638i	−0.959374	+	0.282136i	$0.908957\pi$
$822$		0			0
$823$	−9.85902	−	36.7944i	−0.343664	−	1.28257i	−0.894165	−	0.447737i	$-0.852230\pi$
$823$	−9.85902	−	36.7944i	−0.343664	−	1.28257i	0.550502	−	0.834834i	$-0.314436\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−28.6503	−	28.6503i	−0.996270	−	0.996270i	0.00372312	−	0.999993i	$-0.498815\pi$
$827$	−28.6503	−	28.6503i	−0.996270	−	0.996270i	−0.999993	+	0.00372312i	$0.998815\pi$
$828$		0			0
$829$	−23.8430	+	41.2973i	−0.828102	+	1.43431i	0.0714231	+	0.997446i	$0.477246\pi$
$829$	−23.8430	+	41.2973i	−0.828102	+	1.43431i	−0.899525	+	0.436869i	$0.856087\pi$
$830$		0			0
$831$	10.1292	−	5.84809i	0.351378	−	0.202868i
$832$		0			0
$833$	−29.3305	−	11.7347i	−1.01624	−	0.406582i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	4.37357	−	1.17190i	0.151173	−	0.0405066i
$838$		0			0
$839$	28.8941			0.997534			0.498767	−	0.866736i	$-0.333786\pi$
$839$	28.8941			0.997534			0.498767	+	0.866736i	$0.333786\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$	−24.6687	+	6.60996i	−0.849636	+	0.227659i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−13.6434	+	20.6891i	−0.468791	+	0.710885i
$848$		0			0
$849$	14.7574	−	8.52020i	0.506473	−	0.292413i
$850$		0			0
$851$	4.84248	−	8.38741i	0.165998	−	0.287517i
$852$		0			0
$853$	9.80855	+	9.80855i	0.335838	+	0.335838i	0.854798	−	0.518960i	$-0.173681\pi$
$853$	9.80855	+	9.80855i	0.335838	+	0.335838i	−0.518960	+	0.854798i	$0.673681\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.84777	+	10.6280i	0.0972781	+	0.363047i	0.997355	−	0.0726843i	$-0.0231566\pi$
$857$	2.84777	+	10.6280i	0.0972781	+	0.363047i	−0.900077	+	0.435731i	$0.856490\pi$
$858$		0			0
$859$	3.76197	+	6.51593i	0.128357	+	0.222321i	0.923040	−	0.384704i	$-0.125696\pi$
$859$	3.76197	+	6.51593i	0.128357	+	0.222321i	−0.794683	+	0.607024i	$0.792363\pi$
$860$		0			0
$861$	4.40251	−	3.90835i	0.150037	−	0.133196i
$862$		0			0
$863$	−15.7221	−	4.21271i	−0.535185	−	0.143402i	−0.0189036	−	0.999821i	$-0.506018\pi$
$863$	−15.7221	−	4.21271i	−0.535185	−	0.143402i	−0.516282	+	0.856419i	$0.672684\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	2.38080	−	2.38080i	0.0808560	−	0.0808560i
$868$		0			0
$869$			8.24983i			0.279856i
$870$		0			0
$871$	−26.8872	−	15.5233i	−0.911036	−	0.525987i
$872$		0			0
$873$	−1.29410	+	4.82963i	−0.0437985	+	0.163458i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	7.05332	−	26.3233i	0.238174	−	0.888876i	−0.738519	−	0.674233i	$-0.764474\pi$
$877$	7.05332	−	26.3233i	0.238174	−	0.888876i	0.976693	−	0.214643i	$-0.0688589\pi$
$878$		0			0
$879$	0.525760	+	0.303548i	0.0177334	+	0.0102384i
$880$		0			0
$881$			15.9839i			0.538512i	0.963069	+	0.269256i	$0.0867777\pi$
$881$			15.9839i			0.538512i	−0.963069	+	0.269256i	$0.913222\pi$
$882$		0			0
$883$	−37.9349	+	37.9349i	−1.27661	+	1.27661i	−0.334059	+	0.942552i	$0.608419\pi$
$883$	−37.9349	+	37.9349i	−1.27661	+	1.27661i	−0.942552	+	0.334059i	$0.891581\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−34.9237	−	9.35779i	−1.17262	−	0.314204i	−0.380627	−	0.924729i	$-0.624292\pi$
$887$	−34.9237	−	9.35779i	−1.17262	−	0.314204i	−0.791997	+	0.610525i	$0.790959\pi$
$888$		0			0
$889$	12.6460	−	38.0091i	0.424133	−	1.27478i
$890$		0			0
$891$	2.25649	+	3.90835i	0.0755952	+	0.130935i
$892$		0			0
$893$	16.7375	+	62.4653i	0.560100	+	2.09032i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	24.4486	+	24.4486i	0.816316	+	0.816316i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	47.9433	−	27.6801i	1.59722	−	0.922158i
$902$		0			0
$903$	29.3307	+	1.74399i	0.976065	+	0.0580363i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	26.2923	−	7.04499i	0.873021	−	0.233925i	0.205627	−	0.978630i	$-0.434077\pi$
$907$	26.2923	−	7.04499i	0.873021	−	0.233925i	0.667394	+	0.744705i	$0.267410\pi$
$908$		0			0
$909$	−7.02579			−0.233031
$910$		0			0
$911$	−13.1009			−0.434051			−0.217025	−	0.976166i	$-0.569635\pi$
$911$	−13.1009			−0.434051			−0.217025	+	0.976166i	$0.569635\pi$
$912$		0			0
$913$	69.1107	−	18.5181i	2.28723	−	0.612861i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−32.7831	−	21.6187i	−1.08259	−	0.713913i
$918$		0			0
$919$	−7.08965	+	4.09321i	−0.233866	+	0.135023i	−0.612354	−	0.790583i	$-0.709777\pi$
$919$	−7.08965	+	4.09321i	−0.233866	+	0.135023i	0.378488	+	0.925606i	$0.376444\pi$
$920$		0			0
$921$	−7.94719	+	13.7649i	−0.261869	+	0.453570i
$922$		0			0
$923$	−62.8178	−	62.8178i	−2.06767	−	2.06767i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.07979	+	4.02982i	0.0354648	+	0.132357i
$928$		0			0
$929$	14.8136	+	25.6579i	0.486019	+	0.841810i	0.999871	−	0.0160692i	$-0.00511519\pi$
$929$	14.8136	+	25.6579i	0.486019	+	0.841810i	−0.513852	+	0.857879i	$0.671782\pi$
$930$		0			0
$931$	−34.8987	−	4.16483i	−1.14376	−	0.136497i
$932$		0			0
$933$	1.10253	+	0.295421i	0.0360951	+	0.00967166i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.01202	+	2.01202i	−0.0657298	+	0.0657298i	−0.739208	−	0.673478i	$-0.764800\pi$
$937$	−2.01202	+	2.01202i	−0.0657298	+	0.0657298i	0.673478	+	0.739208i	$0.264800\pi$
$938$		0			0
$939$			4.50147i			0.146900i
$940$		0			0
$941$	−32.2239	−	18.6045i	−1.05047	−	0.606488i	−0.127688	−	0.991814i	$-0.540756\pi$
$941$	−32.2239	−	18.6045i	−1.05047	−	0.606488i	−0.922780	+	0.385326i	$0.874089\pi$
$942$		0			0
$943$	3.22019	−	12.0179i	0.104864	−	0.391357i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.55451	−	24.4618i	0.212993	−	0.794901i	−0.773870	−	0.633344i	$-0.781682\pi$
$947$	6.55451	−	24.4618i	0.212993	−	0.794901i	0.986863	−	0.161557i	$-0.0516516\pi$
$948$		0			0
$949$	23.2463	+	13.4212i	0.754606	+	0.435672i
$950$		0			0
$951$		−	9.69129i		−	0.314262i
$952$		0			0
$953$	23.4345	−	23.4345i	0.759118	−	0.759118i	−0.217044	−	0.976162i	$-0.569641\pi$
$953$	23.4345	−	23.4345i	0.759118	−	0.759118i	0.976162	+	0.217044i	$0.0696414\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.00489	+	2.25838i	0.0647413	+	0.0729270i
$960$		0			0
$961$	−5.24926	−	9.09199i	−0.169331	−	0.293290i
$962$		0			0
$963$	−1.81841	−	6.78639i	−0.0585974	−	0.218688i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	35.2925	+	35.2925i	1.13493	+	1.13493i	0.989346	+	0.145584i	$0.0465062\pi$
$967$	35.2925	+	35.2925i	1.13493	+	1.13493i	0.145584	+	0.989346i	$0.453494\pi$
$968$		0			0
$969$	11.3296	−	19.6234i	0.363959	−	0.630396i
$970$		0			0
$971$	−51.5438	+	29.7588i	−1.65412	+	0.955006i	−0.678765	+	0.734355i	$0.737485\pi$
$971$	−51.5438	+	29.7588i	−1.65412	+	0.955006i	−0.975353	+	0.220651i	$0.929182\pi$
$972$		0			0
$973$	−24.3740	−	48.6795i	−0.781393	−	1.56059i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.3592	+	5.45522i	−0.651348	+	0.174528i	−0.569338	−	0.822103i	$-0.692800\pi$
$977$	−20.3592	+	5.45522i	−0.651348	+	0.174528i	−0.0820096	+	0.996632i	$0.526134\pi$
$978$		0			0
$979$	−35.2766			−1.12744
$980$		0			0
$981$	13.5245			0.431803
$982$		0			0
$983$	35.2967	−	9.45773i	1.12579	−	0.301655i	0.352566	−	0.935787i	$-0.385309\pi$
$983$	35.2967	−	9.45773i	1.12579	−	0.301655i	0.773225	+	0.634132i	$0.218642\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	15.2569	+	30.4709i	0.485631	+	0.969900i
$988$		0			0
$989$	53.7784	−	31.0490i	1.71005	−	0.987299i
$990$		0			0
$991$	14.0903	−	24.4051i	0.447592	−	0.775252i	−0.550637	−	0.834745i	$-0.685615\pi$
$991$	14.0903	−	24.4051i	0.447592	−	0.775252i	0.998229	+	0.0594929i	$0.0189484\pi$
$992$		0			0
$993$	2.69056	+	2.69056i	0.0853823	+	0.0853823i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−6.72258	−	25.0890i	−0.212906	−	0.794577i	−0.986893	−	0.161375i	$-0.948407\pi$
$997$	−6.72258	−	25.0890i	−0.212906	−	0.794577i	0.773987	−	0.633202i	$-0.218260\pi$
$998$		0			0
$999$	0.866025	+	1.50000i	0.0273998	+	0.0474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.c.157.3	✓	24
5.2	odd	4	inner	2100.2.ce.c.493.4	yes	24
5.3	odd	4	inner	2100.2.ce.c.493.2	yes	24
5.4	even	2	inner	2100.2.ce.c.157.4	yes	24
7.5	odd	6	inner	2100.2.ce.c.1657.2	yes	24
35.12	even	12	inner	2100.2.ce.c.1993.4	yes	24
35.19	odd	6	inner	2100.2.ce.c.1657.4	yes	24
35.33	even	12	inner	2100.2.ce.c.1993.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.c.157.3	✓	24	1.1	even	1	trivial
2100.2.ce.c.157.4	yes	24	5.4	even	2	inner
2100.2.ce.c.493.2	yes	24	5.3	odd	4	inner
2100.2.ce.c.493.4	yes	24	5.2	odd	4	inner
2100.2.ce.c.1657.2	yes	24	7.5	odd	6	inner
2100.2.ce.c.1657.4	yes	24	35.19	odd	6	inner
2100.2.ce.c.1993.3	yes	24	35.33	even	12	inner
2100.2.ce.c.1993.4	yes	24	35.12	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{3} +(-1.18454 - 2.36577i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{3} +(-1.18454 - 2.36577i) q^{7} +(0.866025 - 0.500000i) q^{9} +(-2.25649 + 3.90835i) q^{11} +(-4.37238 - 4.37238i) q^{13} +(1.16804 + 4.35920i) q^{17} +(2.51045 + 4.34823i) q^{19} +(1.75649 + 1.97857i) q^{21} +(5.40108 + 1.44721i) q^{23} +(-0.707107 + 0.707107i) q^{27} +(-3.92124 - 2.26393i) q^{31} +(1.16804 - 4.35920i) q^{33} +(0.448288 - 1.67303i) q^{37} +(5.35505 + 3.09174i) q^{39} -2.22509i q^{41} +(7.85281 - 7.85281i) q^{43} +(12.4411 + 3.33357i) q^{47} +(-4.19371 + 5.60471i) q^{49} +(-2.25649 - 3.90835i) q^{51} +(-3.17491 - 11.8489i) q^{53} +(-3.55031 - 3.55031i) q^{57} +(1.11255 - 1.92699i) q^{59} +(6.34248 - 3.66183i) q^{61} +(-2.20873 - 1.45654i) q^{63} +(4.84982 - 1.29950i) q^{67} -5.59161 q^{69} +14.3670 q^{71} +(-4.19308 + 1.12353i) q^{73} +(11.9192 + 0.708707i) q^{77} +(1.58312 - 0.914012i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-11.2105 - 11.2105i) q^{83} +(3.90835 + 6.76946i) q^{89} +(-5.16475 + 15.5233i) q^{91} +(4.37357 + 1.17190i) q^{93} +(-3.53553 + 3.53553i) q^{97} +4.51298i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 8 q^{11} - 4 q^{21} - 60 q^{31} - 8 q^{51} + 84 q^{61} + 112 q^{71} + 12 q^{81} - 136 q^{91}+O(q^{100}) \) 24 * q - 8 * q^11 - 4 * q^21 - 60 * q^31 - 8 * q^51 + 84 * q^61 + 112 * q^71 + 12 * q^81 - 136 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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